We have 3 type of flowers - red, white, pink.
We have to buy flowers to beautify the sidewalk in 5 weeks. The flowers fully develop in 1 week, but during another week flowers die out.
The flowers are crossing like this:
Red + Red = Red + Red + Red + Red
Red + White = Pink + Pink + Pink + Pink
Pink + Pink = Red + White + Pink + Pink
Red + Pink = Red + Pink + Red + Pink
Rules of crossing flowers in each week (in that order):
1. We cross half of red flowers with pink flowers
2. We cross half of white flowers between each other
3. We cross quarter of remaining pink flowers with white flowers
4. We cross remaining white flowers with red flowers
5. We cross half of remaining pink flowers between each other
6. We cross half of remaining red flowers between each other
7. We leave what remains
In 5 weeks we must have at least 84 red flowers, 63 white flowers, 105 pink flowers.
From each color we have to buy at least 1 flower.
Purchased flowers on the beggining are just after of full development.
What is the minimum number of each color of flowers which we have to buy?
Edit: We always round up - I apologize for confusion
White + White = White + White + White + White
White + Pink = White + Pink + White + Pink